Möbius Strip


One of my favorite math activities is the Möbius Strip.   I first saw it demonstrated when I observed a math class taught by Don Buttermore and Don Tomb in 1967 at Gunston Junior High School in Arlington, Virginia.   The Möbius Strip or Möbius Band was named after August Ferdinand Möbius, a nineteenth century German mathematician, who was a pioneer in the field of topology.

You take a long strip of paper, twist one of the ends half a turn, and tape the two ends together.   The result is a circular hoop with the intriguing property of having only one surface and only one edge. (Incidentally, the three-arrow symbol commonly used to denote "recyclable" is in the form of a Mobius strip.)

Giant Möbius Strips have been used as conveyor belts (to make them last longer, since "each side" gets the same amount of wear) and as continuous-loop recording tapes (to double the playing time).   Möbius strips have been used as typewriter ribbons and then as printer ribbons.   In the 1960's Sandia Laboratories used Möbius Strips in the design of versatile electronic resistors.   Möbius strips have been used in advertising -- a flat triangular möbius strip was used as a symbol of EXPO '74;   New Yorker's cover of April 5, 1976 pictured a Möbius Strip around which 30 business people were walking.
And here are some patents based on the Möbius Strip:
Pat. #1,442,632-1923: Lee DeForest: filmstrip -- sound on "both sides";
Pat. #2,479,929-1949: O.H. Harris -- abrasive belt;
Pat. #2,784,834-1957: B.F. Goodrich -- abrasive belt.

Click here for some poems about Möbius Strips:
Möbius Diaper
Möbius Strip

The famous artist, M.C. Escher, used the Möbius strip in several of his works of art:



 

I have used the Möbius strip in my classroom both as a demonstration and as a hands on activity.   I find that
students really enjoy doing this activity on their own.   Either way, I use the following activities:
(1) Make a Möbius strip.
(2) Show its one-sidedness by tracing with a pencil or marker
(3) Show it has only one edge by holding the Möbius strip with one hand and tracing along the edge
(4) Cut the Möbius strip down the center
(5) Make another Möbius strip and cut by starting one-third from one of the edges
(6) This last activity is my favorite -- I saw it demonstrated by Fred Pence at a V2CTM Meeting
      in Harrisonburg, Virginia.   You take two strips (one Möbius and one not) and tape them to each
      other at right angles.   Then cut them both down the middle.

Click here for detailed instructions and photos of these activities

Below is a video of the Mobius Strip:

No Magic At All: Mobius Strip - video powered by Metacafe


Links:

Math Tricks

Mr. P's Puzzles and Games Page